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Strategic competition and collusion Oligopolists need to ensure that they all restrict output – collusion is sustained AND (in the same way as monopolists) they also need to deter entry of new firms

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Sustaining collusion – not so easy in a prisoners dilemma Revision of prisoners dilemma generally and in an oligopoly context

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The prisoners dilemma The payoffs are years in prison Use the underlining method to find the Nash Equilibrium

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The Nash equilibrium The Nash equilibrium is also a dominant strategy equilibrium. So game theorists believe that the predicted outcome is very convincing; confession is a dominant strategy for both players and yet…..

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The equilibrium of the prisoners dilemma The equilibrium is {confess, confess} But both would be better off if neither confessed The dilemma for the prisoners is that they would both be better off if they co-operated with each other (by not confessing) but it is individually rational for them both to confess in any other strategy combination there is an incentive for one of the prisoners to deviate

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A more general interpretation of the prisoners dilemma Confess implies cheating on (or defection from) some mutually beneficial, but not necessarily explicit agreement (to deny): non-cooperation To deny implies some kind of working together or collusion or cooperation between the players

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The generalised PD problem c > a > d > b What is the dominant strategy equilibrium (DSE)?

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The generalised PD problem Since c> a and d > b the DSE is: {not cooperate, not cooperate} But both players would be better off cooperating since a > d Remember that c > a > d > b

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GENERALISATION Any game with this payoff structure is a Prisoners Dilemma The players do not have to be prisoners

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SMALL GROUP WORK Discussion questions on the Prisoners Dilemma Why does the group think so much attention has been given to the prisoners dilemma in (i) economics and (ii) the social sciences more generally? Describe three or more examples of a prisoners dilemma that is faced by real people (acting individually or in groups) in real life. How, if at all, are the prisoners dilemma problems described in (2) above resolved? If they are not resolved in practices how might they be resolved?

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The prisoners dilemma and cooperation/collusion between 2-firms in an Oligopoly (Duopoly) Alpha and Beta are two oil producers who share the market. Each firm has two possible strategies: 1.High output –Lower price 2. Low output – higher price Each chooses its strategy without knowing what strategy the other has chosen (equivalent to simultaneous or hidden moves)

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four possible outcomes: 1.Both produce a high output OK profits (1 billion) 2.Both produce a low output – collusive agreement. E.g. by forming a cartel: Arrangements entered into voluntarily which restrict firms future actions (Alpha and Beta each agree to restrict output to keep prices high). High profits (2 billion) 3.Beta produces low output but Alpha produces high output. Beta has very low profits (0), Alpha very high profits (3) 4.Alpha produces low output but Beta produces high output. Beta has very high profits (3), Alpha very low profits (0) Prisoners dilemma and oligopoly

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Alphas Strategy Betas Strategy Compete on price: high output Dont compete on price: low output Compete on price: high output Dont compete on price: low Output The Prisoners Dilemma and oligopoly collusion 1 0 32 1 3 02 Both firms would improve profits if they colluded to form a cartel in which each agreed to limit price competition and restrict output. But what is the likely outcome (the Nash Equilibrium) of this strategic game?

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Alphas Strategy Betas Strategy Compete on price: high output Dont compete on price: low Output The Prisoners Dilemma and oligopoly collusion 1 0 3 2 1 3 02 Although both firms would have higher profits if they colluded to restrict output there is an incentive for each to cheat because each firm could increase its profits by increasing its output as long as the other firm keeps to the agreement and keeps its own output low. The likely outcome is that they both produce high output. Dont compete on price: low output Compete on price: high output

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Implications Collusion between oligopolists is undesirable but it is also unlikely to be stable firms are likely to be involved in a prisoners dilemma – especially given that collusion is illegal and subject to punishment they can agree to collude BUT this still leaves problem of enforcement. So regulators dont have to worry? Depends - how realistic is the analysis?

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Test your understanding Collusion: Explain why game theorists predict that collusion between oligopolists is likely to be fragile

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Exercise on oligopoly

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Prisoner’s Dilemma An illustration of Nash Equilibrium Art’s Strategies Bob’s Strategies Confess Deny Confess Deny 10 yrs. 1 yr. 3 yrs. 1 yr. 10 yrs.

Prisoner’s Dilemma An illustration of Nash Equilibrium Art’s Strategies Bob’s Strategies Confess Deny Confess Deny 10 yrs. 1 yr. 3 yrs. 1 yr. 10 yrs.

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